(tanθ + cotθ)² = sec²θ + csc²θ
<u>Expand left side</u>: tan²θ + 2tanθcotθ + cot²θ
<u>Evaluate middle term</u>: 2tanθcotθ = = 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
<u>Apply trig identity:</u> tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
<u>Apply trig identity:</u> 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
Answer: 1. 210 meters per second .
2. 756 kilometers per hour.
Step-by-step explanation:
Given : The formula to calculate the estimated speed, in meters per second of a tsunami.
1. If the disturbance occurred at an ocean depth of 4,500 meters.
Then put d= 4500 in the above formula , we get
Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .
Also, A meter per second is equal to 3.6 kilometers per hour.
i.e. 1 meter per second = 3.6 kilometers per hour
Then by unitary method ,
210 meters per second = kilometers per hour
=756 kilometers per hour.